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Journal Articles Journal of the Institute of Mathematics of Jussieu Year : 2022

Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations

Abstract

This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and adapting an argument due to S. N. Kruzkov (1963). Such a result rests on a new weak Poincaré inequality sharing similarities with the one introduced by W.~Wang and L.~Zhang in a series of works about ultraparabolic equations (2009, 2011, 2017). This functional inequality is combined with a classical covering argument recently adapted by L. Silvestre and the second author (2020) to kinetic equations.
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Dates and versions

hal-03133950 , version 1 (07-02-2021)
hal-03133950 , version 2 (22-07-2022)

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Cite

Jessica Guerand, Cyril Imbert. Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. Journal of the Institute of Mathematics of Jussieu, In press, ⟨10.1017/S1474748022000160⟩. ⟨hal-03133950v2⟩
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